There is a continuing and growing need for ceramic or refractory materials in fiber form especially where the material has a high melting temperature. Such fibers are useful as high temperature insulation and even as strengtheners in composites which may have a metal matrix. To date a number of processes for producing fibers have been proposed but most have some disadvantages with respect to the quality and consistency of the fibers or in the economics of their production. For instance, some of the fibers are short and of inconsistent cross section and quality thus restricting their use as strengtheners or high temperature insulation. Other processes may be capable of producing longer lengths of more consistent cross section but are marked by economic disadvantages which seriously restict their usefulness. Still other processes rely on precursor fibers of material which undergoes undesirable phase changes with resultant degradation upon heating to useful temperatures. In accordance with the present improvement long and very thin fibers or filaments of alumina or other ceramic materials can be provided which in the green (unfired) state possess sufficient strength that they can be wound onto spools or otherwise handled with minimal degradation. Since these fibers are comprised of finely divided particles of phase-stable ceramic material, they can be heated to provide ceramic bonding without undesirable high-temperature phase changes. This results in low cost refractory fiber having small diameter and sufficient strength for use as high-temperature insulating material and other applications.